optimal schedule modeling for public transportation systemon city buses for nagpur city for the...

International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064

Index Copernicus Value (2013): 6.14 | Impact Factor (2013): 4.438

Volume 4 Issue 4, April 2015

www.ijsr.net Licensed Under Creative Commons Attribution CC BY

Optimal Schedule Modeling for Public

Transportation System

Neeraj Singh Bais1, Nikhil Pitale

2, Sanket Thorat

3

1M. Tech Transportation Enggineering ,G.H.Raisoni College of Engineering,Nagpur, Maharashtra, India

2, 3Assistant Professor, Civil Engineering G.H.Raisoni College of Engineering Nagpur, Maharashtra, India

Abstract: With rapid development across India, large urban areas have developed. This new metropolitan centers need for

transportation facilities have increased fourfold. As India is a developing country public transport is the most important mode of

transport. But Public transportation in India is inefficient and inadequate. Public transport has not been able to keep pace with the

growing demand for transportation facilities. Therefore it becomes necessary to increase the efficiency of public transport so that more

people can shift from private to public transport. The performance of transportation system can be improved by an Optimal scheduling

of resources. Optimal scheduling can provide economical and efficient use of fleet resource and provide safe and fast mode of transport

to city needs. The proposed method minimizes the waiting time of passengers at stops and to minimize the number of buses require for

the same operation. The constraints include load factor, time constraint & frequency constraint. The optimal schedule will subjected to

condition of maintaining a minimum number of passengers travelling onboard the buses. This will help to increase the frequency if the

demand for service is more and reduce the frequency if demand is less and save considerable amount of money for the agencies. The

proposed model is to be applied to an actual route for Nagpur city.

Keywords: Optimal Scheduling, Public Bus Transport, waiting time,frequency

1. Introduction

With increasing demand in urban centers, demand for public

transport has increased fourfold. This increased requirement

has put tremendous pressure on exiting public transport

infrastructure more so in peak hours. To balance this

capacity is increased which adds to cost and congestion on

urban roads. Hence increasing the capacity is not always a

favorable option. Hence with use of technological

advancements the performance of public transport is

optimized to meet need of increasing demand. Today bus

operations in India are manual and inefficient. This usually

leads to missed or late arrivals to scheduled stops, inefficient

use of resources, and constant decrease in operating speed.

This situation leads to people switching to other mode of

transport which is undesirable.

To increase the performance of transit we provide a better

schedule, which is aligned with load factor or number of

passengers in the bus present upon the capacity of bus. A

good schedule is one which minimize the waiting time of

passengers while maintaining that adequate passenger board

the bus. The following operation is done while working

within a set resources, which acts constraints for the

proposed model. The model is developed such that demands

of both transport system from both the company and user

point of view. Load factor is most important consideration

for the proposed model due to which the number buses will

be increased or decreased according to number of passenger

travelling on the route. The proposed model optimizes the

headway between buses to allow buses to be assigned to

public transport lines in accordance with the demand for the

service o the route. The proposed model is tested in real

condition for a route in Nagpur city.

2. Literature Review

Liang Xu et al. (2012) have developed a system by using

ArcGIS Server technology to provide active bus monitoring

and scheduling system. The method uses 3S technology

GPS, RS, GIS together, to accomplish the on-time location,

information collection and scheduling of the buses. ArcGIS

Server give on-time status of each bus which could be

observed by the user & authorities also it can calculate the

bus arrival time at stops and display distance between two

stops. The entire process is carried out by ArcGIS with no

human interference which helps achieve new optimum level

of optimization. Partha Chakroborty et al (1995) have

proposed a method of optimal scheduling of transit networks

optimization. They used genetic algorithm technique which

is motivated by principles of natural genetics-to solve the

scheduling problem the main advantage of using GAs is that

the problem can be reformulated in a manner that is

computationally more competent than the original problem.

The study presents a number of other benefits which include

optimal resource allocation and scheduling, scheduling

based on fixed vehicle capacity, and network wide optimal

scheduling. Sun chuanjiao et al. (2008) proposed a headway

optimization and scheduling combination of BRT vehicles.

A model based on genetic algorithm is designed to minimize

passengers travel costs and vehicles operation cost. The

method is analyzed check for various parameters such as

Impact of traffic volume and travel speed. The obtained

result shows the method help achieve optimal schedule

performance. Farhan Ahmad Kidwai et al. (2005) have

developed a bus scheduling model using genetic algorithm

for transit network. Genetic algorithms are proposed as the

computational tool because of their ability to handle large

and complex problems. The paper suggest a two phases

solution, first allocation of buses on individual routes with

maximum link flow as the criteria, and second further

reduction of buses on network basis making use of genetic

Paper ID: SUB153499 2053





algorithms as an optimization tool.Tan de-rong et al (2011)

The paper presents a model for optimal scheduling by

rational use of resources & adjusting demand & supply

balance. The paper aims to develop a reasonable departure

interval through the proposed model. The model is tested

and a time table with departure schedule is obtained. Ashish

Verma et al (2006) designed model for optimal integrated

schedules for urban rail & feeder bus operation. The

objective function for schedule coordination is minimization

of the total waiting & transfer time of the commuters. The

function is subjected to limit of load factor and transfer time.

3. Proposed Model

The objective of the scheduling problem is to minimize the

waiting time of passengers at the bus stops and reduce the

number of buses required for the job while maintaining

adequate number of passenger onboard. The proposed

objective is achieved by maximizing the frequency of bus

service. There are, however, certain resource limitations and

service-related constraints that have to be considered while

attempting to achieve the goal of best level of service. The

constraints are as follows, the fleet size, load factor .The

total number of buses is constant. Also for some routes

number of buses maybe fixed. Time constraint includes

minimum stopping time at stops for which bus has to wait

for certain period of time. Also the stopping time should not

be more than higher limit that may cause unease to

passengers. Policy headway is the minimum frequency of

bus service to maintain at all times during day. Policy

headway between two consecutive buses must be less than

or equal to certain limit, provided by government agencies.

As many factors affect scheduling process it is necessary to

make the following assumptions before modelling for public

transportation system. The assumptions are necessary to

maintain a standard over the result of the model. The

assumptions are,

1. The types of the bus models are alike.

2. The passenger’s arrival at the stops obeys uniform

distribution.

3. Each passenger obeys the rule of first come, first on the

bus.

4. The bus pulls in and pulls out on time according to

dispatch time table.

5. The running time between stops must be a certain time; it

cannot change following time period changes.

6. Time loss caused by traffic signal is equal in the same

interval.

7. Departure interval for a time period will remain equal.

8. The fleet size in the model takes no account of vehicle

breakdown and maintenance.

4. Mathematical Formulation

max f = Nm

L∗C

Jj=1

Subject to

a) Load Factor: L=n/C 0.75≤L≤1.25

b) Fleet Size: f ≤Q

Where,

f - Frequency for period j.

Nm - Maximum average number of passengers onboard in

period j.

L – Load factor for period j.

j – Time interval.

C - Capacity of bus.

Q – Maximum number of buses on route.

n – Average number of passenger onboard during period j.

5. Problem Solution

The problem is to maintain an adequate number of

passengers on bus during the time period. The duration of

working hours are divided into time periods and is assumed

to be hourly for the present case. The capacity of each bus is

seating capacity plus the number of standing persons

allowed. Load factor is average number of passenger

travelling on the bus upon its capacity.

The product of Load factor and capacity gives the desired

occupancy for the period j. For the study we had considered

an occupancy of 75% as the minimum frequency to be

maintained at all times. If the load factor is not maintained

for a time period then the number of buses allocated should

be reduced for the same period. Although a minimum

frequency of buses is to be maintained at all times to avoid

the discomfort to passengers.

The maximum number of passenger onboard for a time

period is taken from the data collected at stop. The stop

location on a route is selected such that it has maximum

number of passenger boarding. The maximum value for total

number of passenger for period is taken from the collected

data for the duration of study.

6. Testing Proposed Model

The proposed method is applied to a real world conditions

on city buses for Nagpur city for the Bardi to Hingna route.

The city buses run to and from Bardi to Hingna starting at

6:00am to 10:00pm. The length of route is 16 km and total

of 20 buses run daily. The round trip travel time for the route

is 1.5 hours (110 minutes) with 27 stops.

The peak hour is considered between 8:00 am to 11:00 am

and 5:00 pm to 7:00pm .the frequency for peak hour is 8

buses while for non peak hours it is 6 buses with an interval

of 10 minutes in between them. The buses can carry 58

passengers in which 44 are seated and 14 standees.

Table 1: Timetable Of Bardi To Hingna Route Direction Start Time

Bardi to Hingna 6:00 6:10 6:20 6:30 6:40 6:50

...... 21:40 21:50 22:00 22:15 22:30

Hingna to Bardi 6:05 6:20 6:30 6:40 6:50 7:00

....... 22:35 22:45 22:55 23:05 23:25

The stop selected to measure the maximum load is

morbhavan stop. The data was collected for working and

non working day throughout the schedule run time. The

average maximum numbers of passenger boarding the bus

are shown in following graph.






Figure 1: Average Number of Passenger at Stop.

The maximum value for number of passenger for a

particular period is chosen from the set of reading for the

same period from study days. The average number of

passenger a bus carries during that period gives the load

factor for that period. From the study it has been seen

schedule can be made for working days and non working

days with a reduced frequency. The schedule is drawn for

each time period so as cater to that specific period demand.

7. Conclusion

From the result of the proposed model we have been able to

form an optimal schedule while maintaining a percent load

factor. The frequency is optimized according to passenger

demand which means increase the level of service; while

where the frequency is reduced it would lead to more load

on running buses.

Refrences

[1] Ashish Verma et al (2006) “Developing Integrated

Schedules for Urban Rail and Feeder Bus Operation” J.

Urban Plann. Dev. 2006.132:138-146.

[2] Tan De-Rong et al (2011) “The Optimization of Bus

Scheduling Based on Genetic Algorithm” International

Conference on Transportation, Mechanical, And

Electrical Engineering (TMEE).

[3] Sun Chuanjiao et al (2008) “Scheduling Combination

and Headway Optimization of Bus Rapid Transit” J

Transpn Sys Eng & It, 2008, 8(5), 61_6.

[4] Farhan Ahmad Kidwai et al(2005) “A Genetic

Algorithm Based Bus Scheduling Model For Transit

Network” Eastern Asia Society for Transportation

Studies, Vol. 5, pp. 477 – 489.

[5] Partha Chakroborty et al (2012) “Principal of

Transportation Engineering” PHI pp.171-197.

[6] Avishai Ceder (2007) “Public Transit Planning and

Operation” Butterworth-Heinemann.

[7] Kalyanmoy Deb et al (1995) “Optimal Scheduling of

Urban Transit Systems Using Genetic Algorithms”

Journal of Transportation Engineering /

November/December.

[8] YANG Hairong et al (2009) “Optimal Regional Bus

Timetables Using Improved Genetic Algorithm” Second

International Conference on Intelligent Computation

Technology and Automation.

[9] Angel Ibeas et al (2013) “Bus Size and Headways

Optimization Model Considering Elastic Demand” J.

Transp. Eng. 2014.140.

[10] Alireza Khani et al (2011) “Transfer Optimization in

Transit Networks: Headway and Departure Time

Coordination” 14th International IEEE Conference on

Intelligent Transportation Systems Washington, DC,

USA. October 5-7, 2011.

[11] Angel Ibeas, Borja Alonso2; Luigi dell’Olio and Jose

Luis Moura “Bus Size and Headways Optimization

Model Considering Elastic Demand” Journal of

Transportation Engineering, ASCE, ISSN 0733-

947X/04013021(9)

[12] Yadan Yan et al (2013) “Robust Optimization Model of

Bus Transit Network Design with Stochastic Travel

Time “Journal of Transportation Engineering, Vol. 139,

No. 6, June 1, 2013.©ASCE, ISSN 0733-947X/2013

[13] Liping Fu et al “Real-Time Optimization Model for

Dynamic Scheduling of Transit Operations”

Transportation Research Record 1857 Paper No. 03-

3697.

Author profile Neeraj Singh Bais student of masters in

Transportation Engineering from G.H.Raisoni college

of Engineering,Nagpur.






Table 2: schedule for working day Working Day Schedule

Time Range Frequency Departure Interval(Minutes) Time Range Frequency Departure Interval(Minutes)

6:00 - 7:00 4 15 2:00 - 3:00 5 12

7:00 - 8:00 6 10 3:00 - 4:00 5 12

8:00 - 9:00 8 7.5 4:00 - 5:00 6 10

9:00 - 10:00 8 7.5 5:00 - 6:00 8 7.5

10:00 -11:00 8 7.5 6:00 - 7:00 8 7.5

11:00 -12:00 6 10 7:00 - 8:00 8 7.5

12:00 - 1:00 6 10 8:00 - 9:00 6 10

1:00 - 2:00 6 10 9:00 - 10:00 5 12

Table 3: schedule for non working day Non-Working Day Schedule

Time Range Frequency Departure Interval(Minutes) Time Range Frequency Departure Interval(Minutes)

6:00 - 7:00 4 15 2:00 - 3:00 5 12

7:00 - 8:00 5 12 3:00 - 4:00 5 12

8:00 - 9:00 6 10 4:00 - 5:00 5 10

9:00 - 10:00 6 10 5:00 - 6:00 7 09

10:00 -11:00 6 10 6:00 - 7:00 7 09

11:00 -12:00 6 10 7:00 - 8:00 7 09

12:00 - 1:00 6 10 8:00 - 9:00 5 12

1:00 - 2:00 5 10 9:00 - 10:00 5 12


optimal schedule modeling for public transportation systemon city buses for nagpur city for the...

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